System and method for digital image intensity correction

ABSTRACT

The present invention provides a method and apparatus to enhance the image contrast of a digital image device while simultaneously compensating for image intensity inhomogeneity, regardless of the source. The present invention corrects intensity inhomogeneities producing a more uniform image appearance. Also, the image is enhanced through increased contrast, e.g., tissue contrast in a medical image. The method makes no assumptions as to the source of the inhomogeneities, e.g., physical device characteristics or positioning of the object being imaged. In the method, the error between the histogram of the spatially-weighted original image and a specified histogram is minimized. The specified histogram may be selected to increase contrast generally or particularly for accentuation, e.g., on localized regions of interest. The weighting is preferably achieved by two-dimensional interpolation of a sparse grid of control points overlaying the image. A sparse grid is used rather than a dense one to compensate for slowly-varying image non-uniformity. Also, sparseness reduces the computational complexity, as the final weight set involves the solution of simultaneous linear equations whose number is the size of the chosen grid.

This application is a Continuation application and claims the benefit ofU.S. patent application Ser. No. 11/536,594 filed Sep. 28, 2006 nowabandoned, the contents of which are incorporated herein by reference.

BACKGROUND OF THE PRESENT INVENTION

1. Technical Field

The technical field generally relates to digital imaging and morespecifically to a method for improving the image contrast of a digitalimage.

2. Background

With the rise of digital imagery, the usage of digital imagingtechniques has spread to almost all scientific, corporate and numerousother endeavors. The usage of imaging and the improvements thereon canbe more important in some industries, e.g., life sciences, and mostimportant in others, e.g., medical and dental imaging. Physicians andsurgeons, for example, have begun to rely on digital imagery overconventional techniques, and the rise of computers and digitization haveaccelerated the paradigm shift to the new medium. Naturally,improvements in the quality of digital images have been felt in theconsumer industries, e.g., sales of improved digital cameras and toolsto visualize images, and in numerous commercial applications.

As digital imaging surpasses and supplants all other forms of medicaland other imaging, e.g., use of film and chemical processes,improvements in the quality of digital images will be key. In themedical and dental areas, for example, a variety of imaging techniqueshave been and are currently employed to best capture the detail of thehuman body tissue, permitting those skilled in interpreting these imagesto diagnose various illnesses, e.g., cancer, from a subtle shade in theimage. Inhomogeneities in the image intensity can even compromisediagnosis and cause delays in treatment, demonstrating the importance ofthe need for improvements in imaging techniques. Of course, imageintensity inhomogeneities cause multiple other problems in non-medicalareas requiring image interpretation or fine resolution, e.g.,photography.

Although the contemplated imaging improvement techniques of the instantinvention are applicable to all images having intensity inhomogeneitiestherein, Applicant will describe in detail technologies where theimprovements in imaging are quite critical, e.g., medical diagnosis.Specific improvements in correcting digital image intensityinhomogeneities are also set forth in Applicant's co-pendingapplication, U.S. patent application Ser. No. 11/452,415, filed Jun. 14,2006, incorporated by reference herein. Although a focus of the presentapplication herein is medical imaging, the principles of the instantinvention are applicable to all digital imaging, particularly whereimage intensity inhomogeneities are present.

For example, magnetic resonance (MR) imaging techniques employ receiversand computers to gather, process and display the data collected. As iswell understood in the MR art, in MR imaging or MRI, atomic nuclei in asample are exposed to magnetic fields, and variations in atomicresponses are detected, positions calculated and effects visualized formedical diagnosis. The numerous advantages of MRI and technical detailsthereof are found in various issued patents obtained by Applicant'sassignee.

The problems associated with MRI image intensity inhomogeneity are wellknown. Images that exhibit this phenomenon show gradual, low frequencyspatial variation in intensity within the localized regions of anatomyor other areas of interest. The sources of the problem in MRI imaginginclude various component parts of an MR device, such as the receivercoil, transmitter coil and magnetic field variations, uncompensated eddycurrents, and patient positioning. Display presentation and automaticcomputer analysis, including tissue segmentation and classification,become problematic with such images. In other arts, the sources of imageintensity inhomogeneities will differ, e.g., glare from the sun or otherlight source, but the principles of the present application, as claimed,apply in the same or similar fashion.

As is understood in the MRI art, the receiver coil may be the primarycontributor to intensity variations. The spatial variation of the coilfield produces images that have strong signal intensities near the coilsurface and decreased intensity distant from the coil. Both conventionalcircumferential coils and, particularly, surface coil arrays may exhibitthis problem. It should, of course, be understood that in othertechnological usages image intensity variations can be introduced intoimages from a variety of sources, requiring a technique to adapt to andcorrect such variations.

A simple mathematical model of a digital image, e.g., the measured MRimage, is given by the following equation:R(x,y)=F(x,y)·I(x,y)where R(x,y) is the received image, F(x,y) is the multiplicative,inhomogeneous coil field, and I(x,y) is the unadulterated true imagedata. In this model random noise is ignored. If the coil field wereknown, the received image could be modified by F⁻¹(x,y) producing a moreuniform true image. Numerous methods to estimate the receiver coil fieldhave been proposed. One group or class of solutions involves knowledgeof the coil geometry and electrical characteristics, allowing analyticfield modeling using the Biot-Savart law. These methods, however,require knowledge of the patient position and size of the receiver coiland do not account for changing coil characteristics. Also, the flexiblenature of coil arrays is problematic. Another class utilizes additionalmeasurements on a uniform phantom to map the coil field. The requirementfor identical patient and phantom scanning parameters make thesetechniques impractical. Other techniques use low resolution imagesacquired at the time of the patient scan to estimate the coil field,thus increasing the scan time. Post-processing or retrospective methodshave been proposed also. Some require manual intervention to achievegood results, which is not desirable. Some assume that a low passfiltered version of the image is a good approximation to the coil field,which is not the case in high contrast areas of images.

It should, of course, be understood that F(x,y) in other technologicalareas represents other multiplicative, inhomogeneous sources of datavariation. A number of other post-processing techniques use imagecontent to generate an estimate of the distortion. Thus, a system,device and method are desired that compensate for image intensityinhomogeneity regardless of the source while simultaneously enhancingthe image contrast.

Although the imaging arts, whether medical or other, are quitesophisticated, image intensity inhomogeneities and other such artifactscontinue to haunt the digital imaging field. Although the need forquality imaging is more pronounced in medicine, the principles set forthin the present invention, representing a significant advance in digitalimaging per se, are applicable to all uses of digital imaging.

SUMMARY

The present invention provides a method, apparatus and system to enhancethe image contrast of a digital image device while simultaneouslycompensating for image intensity inhomogeneity, regardless of thesource. The present invention corrects intensity inhomogeneitiesproducing a more uniform image appearance. Also, the image is enhancedthrough increased contrast, e.g., tissue contrast in a medical image.The present invention makes no assumptions as to the source of theinhomogeneities, e.g., physical device characteristics or positioning ofthe object being imaged. In the method, the error between the histogramof the spatially-weighted original image and a specified histogram isminimized. The specified histogram may be selected to increase contrastgenerally or particularly for accentuation, e.g., on localized regionsof interest. The weighting is preferably achieved by two-dimensionalinterpolation of a sparse grid of control points overlaying the image. Asparse grid is used rather than a dense one to compensate forslowly-varying image non-uniformity. Also, sparseness reduces thecomputational complexity, as the final weight set involves the solutionof simultaneous linear equations whose number is the size of the chosengrid.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, aspects, and advantages of the present invention willbecome better understood with regard to the following description,appended claims, and accompanying drawings where:

FIGS. 1A and 1B generally illustrate an MRI apparatus, exemplary of asystem where image intensity inhomogeneities are present;

FIG. 2 illustrates a sagittal lumbar spine T1 fast spin echo image withintensity variations;

FIG. 3 shows a histogram for the image of FIG. 2;

FIG. 4 illustrates a uniform histogram equalized image of the image ofFIG. 2;

FIG. 5 shows a uniform histogram for the image of FIG. 4, weighted tobrighter values;

FIG. 6 illustrates an image processed according to the presentinvention;

FIG. 7 shows a histogram, according to the present invention, for theimage of FIG. 6;

FIG. 8 shows the weighting function surface of the present invention;and

FIG. 9 illustrates a flow chart of steps employed in implementing anembodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The following detailed description is presented to enable any personskilled in the art to make and use the invention. For purposes ofexplanation, specific nomenclature is set forth to provide a thoroughunderstanding of the present invention. However, it will be apparent toone skilled in the art that these specific details are not required topractice the invention. Descriptions of specific applications areprovided only as representative examples. Various modifications to thepreferred embodiments will be readily apparent to one skilled in theart, and the general principles defined herein may be applied to otherembodiments and applications without departing from the scope of theinvention. The present invention is not intended to be limited to theembodiments shown, but is to be accorded the widest possible scopeconsistent with the principles and features disclosed herein.

The present invention is an imaging method, apparatus and system thattransforms the original pixel values of an image so that the resultingimage histogram approximates a specified histogram with certain spatialconstraints. Histogram modification has been used as an imageenhancement technique for some time. By modifying the histogram asdescribed below, however, the method of the present inventioncompensates for image intensity inhomogeneity regardless of the source,while simultaneously enhancing the image contrast. The present inventionwill be described in more detail hereinbelow with particular referenceto a specific medical device employing imaging, i.e., a magneticresonance imaging (MRI) device.

It should, of course, be understood that although the presentdescription describes MRI applications of the principles of the presentinvention in some detail, it is understood by those of skill in thedigital imaging arts that the principles and teachings of the presentinvention are applicable to numerous other industries and softwareimaging applications, whether medical, dental or other life sciencesapplications. Indeed, the problems of correcting image intensityinhomogeneities plague all industries reliant on images, digital andotherwise, the medical diagnostic area being a more critical one.

With the above in mind, an exemplary MRI apparatus which employs andillustrates the principles of the present invention is shown in FIGS. 1Aand 1B of the Drawings. In an open MRI, generally represented by thereference numeral 100 in FIGS. 1A and 1B, a magnet structure includes apair of vertically extending sidewalls 102 and an upper flux returnstructure, including a pair of flux return members 104 and 106 extendingbetween sidewalls 102. The lower flux return structure includes asimilar pair of flux return members 108 and 110. A pair of round,generally cylindrical ferromagnetic poles 112 project inwardly from theopposed sidewalls 102 along a magnet axis or pole axis 114. A fluxsource is also provided, in this example including coils 116,illustrated in FIG. 1B, which may be resistive or super-conducting coilssurrounding the poles or may be permanent magnet material, as isunderstood in the art. In a possible variant, the upper and lower fluxreturn members, 104, 106, 108 and 110 may not necessarily include pairs,as is described hereinabove. In particular the upper and lower fluxreturn members may include a single member that is positioned and sizedto provide an adequate flux return path.

A more detailed description of the exemplary MRI apparatus may be foundin commonly-owned U.S. Pat. No. 6,828,792, which is incorporated byreference herein, as well as the aforementioned and commonly-owned U.S.patent application Ser. No. 11/452,415, filed Jun. 14, 2006, alsoincorporated herein by reference. As discussed, the principles of thepresent innovation are just as applicable for any imaging device andtechnique where image intensity inhomogeneity is a problem.

In an MR image, for example, intensity inhomogeneity decreases imagecontrast, thereby making presentation problematic regardless of contrastand brightness settings. An example of an image with undesirableintensity variations is shown in FIG. 2. The image of FIG. 2 is from anMRI apparatus, such as that of FIGS. 1A and 1B, and shows a sagittallumbar spine T1 fast spin echo image. Areas of the image near thereceiver coil are extremely bright with intensity decreasing withanterior distance. The histogram of this image is shown in FIG. 3. Thedominance of the dark pixel areas is noted with the great majority ofpixels below intensity values of 1000.

After processing the image according to traditional uniform histogramequalization, the image is more uniform in intensity, but still somewhatdifficult to analyze, as is shown in FIG. 4. The modified histogram ofthis image is shown in FIG. 5. As can be seen from FIGS. 4 and 5, thehistogram is more uniformly distributed and the resulting image is moreuniform in appearance, albeit not demonstrably better than the original.

In the traditional method of direct histogram specification, thehistogram is modified in a manner that depends solely on the globalproperties of the image, i.e., the histogram. This traditional techniquetransforms the image histogram to a specified histogram without regardto local image content. Two distinct images with identical histogramswill, therefore, generate the same transformation.

Although this is a standard method of image enhancement, it is notentirely appropriate for the aforedescribed image intensityinhomogeneity intensity problem. A “dark” pixel in the relatively brightportion of an MR or other digital image should not be transformed in thesame way as a “dark” pixel in an area of decreased intensity. To remedythis problem, the present invention introduces the effects of theslowly-varying intensity inhomogeneity into the generation of individualpixel transformations.

Before correction, near the surface of the receiver coil 116 of an MRIdevice, image intensity is bright, while image intensity drops offmoving away from the coil. When corrected using the correction techniqueof the present invention, the intensity near the coil is decreased whilethe intensity away from the coil is increased. This technique makes theimage intensity more uniform, and decreases image contrast globally, butincreases contrast within localized regions of anatomy or other areas ofinterest. Following correction, images of the spine and images of tissueregions with fat have greater contrast and with the cerebellum moredetail, e.g., where the head is close to the coil. Prior to correction,areas with high intensity, such as subcutaneous fat, bright areas nearthe skin, and bright areas such as the brain near the coil, distort orcompromise the image and make diagnosis difficult. After processing, theglobal image contrast is decreased, and the intensity of the fat valuesis decreased, but dark areas in fat are increased and contrast withinlocalized regions of anatomy is increased. Similarly, in other imagingcontexts, manipulation of the image contrast pursuant to the teachingsof the present invention will smooth out image intensity inhomogeneitiesand improve overall image contrast.

In the present invention, a specified histogram distribution is selectedto enhance the image in some way. Uniform or linearly-rising histogramshave been used to increase the contrast in dark image areas, but anyother shape may be used. A transformation is then applied to theoriginal image gray levels modifying them to have the specifiedhistogram. These are the reference pixel set. A sparse rectangular gridof control points is then overlaid on the image. This grid representsthe location of a group of interpolating functions that influence eachpixel's final value depending on the Euclidean distance of the pixelfrom the control or grid point. A sparse grid is chosen rather than adense one to compensate for the slowly varying image intensityinhomogeneity. A dense grid would introduce the capability to correctfor high frequency changes in image intensity, which is not necessarilydesirable.

The method of the present invention computes a set of weights that scalethe amplitudes of the interpolating functions. The weights are computedin such a way as to minimize the sum of the squared errors between thehistogram-transformed pixel value and the weighted pixel value. Gridsparseness reduces the computational complexity as the final weight setinvolves the solution of simultaneous linear equations whose number isthe size of the chosen grid. As indicated, particular histograms may beemployed for desired effect. For example, a specified histogram mayinclude a tissue contrast enhancement histogram, e.g., bathtub-shaped toenhance images where there are predominantly two ranges of interestingintensities, light and dark representing two distinct tissues. A tissueaccentuation histogram could be a rectangular histogram centered in themid-gray levels meant to subdue both light and dark pixels outside thetissue of interest thereby enhancing intra-tissue contrast. Similarly, alinearly-rising histogram may be employed, as well as combinations ofthe aforementioned histograms to achieve a variety of effects.

The global histogram specification transformation is computed in theconventional manner:s _(n) =T(G _(n))where n is the gray level index, s_(n) is the gray level result aftertransforming gray level value G_(n), and T(·) is the histogram-specifiedtransformation.

The square of the total image error is given by:

$ɛ^{2} = {{\sum\limits_{i = 1}^{N}\; ɛ_{i}^{2}} = {\sum\limits_{i = 1}^{N}\;\left( {s_{i} - s_{i}^{\prime}} \right)^{2}}}$where ε_(i) ² is the squared error associated with the i^(th) pixel, Nisthe number of pixels in the image, and s_(i) is the histogram-specifiedtransformed gray level of the i^(th) pixel. The term s_(i)′ is theresulting gray level of the i^(th) pixel due to the total contributionof the interpolated weighting grid. Thus,

$s_{i}^{\prime} = {P_{i}{\sum\limits_{j = 1}^{M}\;{b_{j\; i}W_{j}}}}$where P_(i) is the original gray level of the i^(th) pixel, b_(ji) isthe interpolation coefficient of the j^(th) grid point acting on thei^(th) pixel, W_(j) is the weight value of the j^(th) interpolatingfunction, i.e., grid point, and M is the number of points in the grid.That is, the new gray level value of the i^(th) pixel is the old grayvalue times the sum of the M interpolation function contributions.Two-dimensional interpolation functions have been studied, andmultiquadratic basis functions are preferably chosen for theirsmoothness and accuracy. In that case, the equation used isb_(ji)=√{square root over ((d_(ji) ²+r²))}, where r is an adjustableparameter, and d_(ji) is the Euclidean distance from the j^(th) gridpoint to the i^(th) pixel. Other functions such as b_(ji)=d_(ji) ² logd_(ji) or two-dimensional Gaussian functions may be used for simplicity.

The total squared error then becomes:

$ɛ^{2} = {\sum\limits_{i = 1}^{N}\left\lbrack {s_{i} - {P_{i}{\sum\limits_{j = 1}^{M}\;{b_{j\; i}W_{j}}}}} \right\rbrack^{2}}$

Taking the partial derivative with respect to the weights and equatingto zero minimizes the error, yielding:

$\frac{\partial ɛ^{2}}{\partial W_{k}} = {{2{\sum\limits_{i = 1}^{N}{\left\lbrack {s_{i} - {P_{i}{\sum\limits_{j = 1}^{M}\;{b_{j\; i}W_{j}}}}} \right\rbrack \cdot \left\lbrack {{- P_{i}}b_{k\; i}} \right\rbrack}}} = 0}$${\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{k\; i}{\sum\limits_{j = 1}^{M}\;{b_{j\; i}W_{j}}}}} = {\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{k\; i}}}$

This may be rewritten in matrix form as

${\begin{bmatrix}{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}^{2}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{M\; i}}} \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2\; i}^{2}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2i}b_{M\; i}}} \\\vdots & \vdots & \; & \vdots \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{1i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}^{2}}}\end{bmatrix}\begin{bmatrix}W_{1} \\W_{2} \\\vdots \\W_{M}\end{bmatrix}} = \begin{bmatrix}{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{1i}}} \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{2i}}} \\\vdots \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{M\; i}}}\end{bmatrix}$   B W = ZB is a symmetric and positive definite matrix and the set of weights cannow be solved by the inversion of B.W=B⁻¹Z

The image of FIG. 2 was processed with the technique describedhereinabove and the resulting image is shown in FIG. 6. As is evidentfrom the modified figure, the image has been transformed to a moreuniform intensity. Unlike the traditional histogram equalizationtechnique, the method of the present invention considers a pixel'slocation when performing modification. The resulting histogram is shownin FIG. 7. The histogram still shows a large number of pixels near zerointensity, representing those in the image outside the anatomy. However,there has been a shift in anatomy pixels toward brighter values.

The image of FIG. 7 was processed using two-dimensional Gaussianweighting functions centered on a 4×4 grid. That is, 16 grid points werechosen to overlay the original image information of FIG. 2. At each gridpoint, the interpolation function or weighting function used was atwo-dimensional Gaussian function. Alternatively, for a 3D MR image, theinterpolation function or weighting function used at each 3D grid pointcould be a three-dimensional Gaussian function. Each weighting functionat each grid point varies in amplitude, thereby correcting the originalimage for intensity inhomogeneities.

The total weight contribution to the image of these functions is shownin FIG. 8. The brighter intensity areas represent the higher weightingvalues. The weighting surface appears to be the inverse of the coilintensity profile in the original image. The weighting functions arecentered at the intersection of the gridlines, i.e., the intersectionsof horizontal and vertical lines connecting the 16 grid points, alongthe image perimeter as well as with each other.

The method described hereinabove corrects intensity inhomogeneitiesproducing a more uniform image appearance. Also, the image is enhancedthrough increased contrasting, e.g., tissue contrast. The method makesno assumptions as to the source of the inhomogeneities, e.g., physicalcoil characteristics or patient placement in medical applications orobject positioning in other applications. In the method of the presentinvention, the error between the histogram of the spatially-weightedoriginal image and a specified histogram is minimized. The specifiedhistogram may be selected to increase contrast generally or toaccentuate a particular image type or class, e.g., in MRI a particularlocalized region of anatomy or other area of interest. The weighting isachieved by two-dimensional interpolation of a sparse grid of controlpoints overlaying the image. The sparse grid is used rather than a denseone to compensate for the slowly-varying image non-uniformity. Also,sparseness reduces the computational complexity as the final weight setinvolves the solution of simultaneous linear equations whose number isthe size of the chosen grid.

With reference now to FIG. 9 of the Drawings, there is shown aflowchart, designated generally by the reference numeral 900,illustrating various steps that may be performed in implementing thepresent invention. In FIG. 9, original image gray levels, i.e., the rawimage data or P_(i), designated by the reference numeral 905, such asshown hereinabove in FIG. 2, are used to generate an original imagehistogram 910, such as shown in FIG. 3. Also shown in FIG. 9 is aspecified histogram 915, e.g., the aforementioned uniform,linearly-rising or other histograms. A transformation 920 is thenapplied to the original gray levels 905, using the original imagehistogram 910, modifying the levels to have the specified histogram 915,resulting in modified image gray levels 925.

Also shown in flowchart 900 of FIG. 9 are image pixel locations,designated by the reference number 930, which correlate to theaforedescribed grid, particularly a sparse rectangular grid of controlpoints, overlaid on the image. As described hereinabove, the gridincorporates interpolation functions, designated generally by thereference numeral 935, which are used in the matrix calculations.

The original image gray levels (P_(i)) 905 and the grid functions 935are used to compute the aforedescribed B matrix, designated by thereference numeral 940, which is then inverted 945. The original imagegray levels 905, grid interpolation coefficients/functions 935 and themodified or transformed image gray levels 925 are employed to computethe aforementioned Z vector, designated by reference numeral 950. Theinverted B matrix 945 and Z vector 950 are then used to compute theweight vector W, designated by reference numeral 955, as per theaforedescribed formula:W=B ⁻¹Z.

The original image gray levels 905, the grid functions 935 and theweight vector (W) 955 are then employed to modify the original data, themodification operation being designated by reference numeral 960, thusproducing output-corrected image gray levels 965, pursuant to theteachings of the present invention. The resultant image, adjusted perthe steps of FIG. 9, offsets and corrects the aforementioned intensityinhomogeneities in the original pixel information, providing significantenhancements in the field of digital imaging, and providing healthcareand MRI treatment professionals with a better diagnostic tool forinterpreting MRI imagery or any digitally-produced imagery.

Additional applications of the present invention in the medical arenainclude endoscopic viewing, where an endoscope is inserted into the bodywith a camera and source of illumination at the leading end. The imagesproduced by this approach may be non-uniform in intensity, e.g., withthe edges of the image darker than the center. The techniques of thepresent invention can be applied to such images, correcting thenon-uniformities therein, providing greater contrast for imageinterpretation, and facilitating diagnoses. An additional application isin the area of ultrasound imaging, where the principles of the presentinvention would be applicable.

As discussed, the principles and techniques of the present invention areapplicable to all digital imaging situations where the digital image hasintensity inhomogeneities therein, regardless of the source of theintroduced error. The numerical correction techniques of the instantinvention, as well as apparatus implementing them, are therefore quiteuseful for a large variety of industries beyond medical and dental.

In the consumer sector, the dramatic rise in digital cameras and thesupplantation of the traditional chemical film industry, whether instill pictures or video, has been a revolution, the speed of which isincreasing. Despite the rapid rate and numerous advances in the digitalarena, however, several problems from the analog world remain, as wellas new problems being encountered. The principles of the presentinvention are adaptable to correct the imaging intensity inhomogeneityissues arising in this new consumer products market.

For example, digital cameras have a flash adapter for use in lowillumination environments. In wide angle or landscape modes, the sidesof the image are considerably darker than the center portion, withdetail falling off along the sides with the lack of contrast. Theprinciples of the present invention, set forth hereinabove, areapplicable and helpful in processing these digital images. Illuminationcorrection, for example, can be done at a photo processing shop, orediting using computer application software. Alternatively, thealgorithms and techniques can be incorporated directly into the cameraitself, allowing immediate post-processing or automatic correcting ofimages containing intensity inhomogeneities and contrast problemstherein.

The weighing and sparse grid features of the present invention can alsobe useful in other situations where digital cameras would be employed topreserve the moment in difficult lighting environments. For example, atlarge concerts such as in stadiums, the stage is illuminated buteverything else is considerably darker, especially at night or indarkened arenas. In night imaging, and other areas of image intensityinhomogeneity, the camera will automatically correct the image byaveraging the values of the pixels. However, when the average intensityis less than the subject area, the camera increases the exposure,washing out the subject. Thus, with existing digital imaging techniques,the image pixels are averaged and considerable detail is lost.Utilization of the improvements set forth in the present invention,providing an improved analysis and correction of local distortions, willameliorate the image inconsistencies and allow better preservation ofsignificant moments in peoples' lives, whether close up to abrightly-lit stage or far therefrom.

As indicated, the intensity of the sun can create serious imagedistortion, which is correctable using the principles of the presentinvention. Another application of the imaging corrective feature of thepresent invention is in the field of satellite imaging and topographicanalysis. Here, as in medical imaging, fine details as to terrain can beof great importance, e.g., in municipal planning, governmental studies,and, of course, to the military and surveillance agencies. Extractinginformation from images, whether from the air or satellite, and gleaningintelligence therefrom, is of great use to select individuals andorganizations.

Although the principles of the present application are describedprimarily in the context of still imagery, e.g., an MRI or a digitalphoto, the techniques of the present invention are also applicable tovideo and motion picture films. As indicated, the images in the framesor discrete units of a movie can be cleaned up in post-processing, or,with adequate computational capacity, corrected on-the-fly. It should,of course, be understood that the techniques of the present inventioncan be adapted in such applications to take advantage of a number ofsimilar adjacent image frames, providing a greater sample formeasurements and corrective actions. For example, the same or similarcorrective actions taken in one frame can be applied in another.

Additionally, in the conversion of analog images to digital, there is achance that inhomogeneities within the analog medium, e.g., film, maytransfer to the digital realm. These irregularities may be detectableprior to processing, allowing the corrective techniques of the presentinvention to ameliorate or eliminate the artifacts. Of course, onceconverted to digital, the principles of the present invention, set forthin detail hereinabove, are then readily applicable.

An additional benefit of the instant invention is that the algorithmsemployed on an image only correct intensity or other inhomogeneitiespresent. If the native image has no such inhomogeneities present, theprinciples of the present application do not then cause harm orotherwise compromise that image.

The foregoing description of the present invention provides illustrationand description, but is not intended to be exhaustive or to limit theinvention to the precise one disclosed. Modifications and variations arepossible consistent with the above teachings or may be acquired frompractice of the invention. Thus, it is noted that the scope of theinvention is defined by the claims and their equivalents.

1. An imaging apparatus for imaging an object, said apparatuscomprising: scanning means for scanning said object and receiving imagedata of said object; generation means for generating a histogram of aportion of said image data; and transformation means for transformingimage pixel information in said image data of said portion by minimizingerror between said histogram and specified histogram, wherein saidtransformation is not uniformly applied to said image data of saidportion, wherein a plurality of grid points overlay said image portionof said object, each said grid point having associated therewith atleast one interpolating function, thereby minimizing said error.
 2. Theimaging apparatus according to claim 1, wherein said processortransforms image pixel information by weighting each pixel according toa weighting function.
 3. The imaging apparatus according to claim 2,wherein said weighting vector (W) is described by the formula:W=B⁻¹Z.
 4. The imaging apparatus according to claim 3, wherein matrix Band vector Z are described by the formulas: $B = {\begin{bmatrix}{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}^{2}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{M\; i}}} \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2\; i}^{2}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2i}b_{M\; i}}} \\\vdots & \vdots & \; & \vdots \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{1i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}^{2}}}\end{bmatrix}\mspace{20mu}{and}}$ $Z = \begin{bmatrix}{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{1i}}} \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{2i}}} \\\vdots \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{M\; i}}}\end{bmatrix}$ where s_(i) is the histogram specified transformed graylevel of the i^(th) pixel, N is the number of pixels in the image, P_(i)is the original gray level of the i^(th) pixel, b_(ji) is theinterpolation coefficient of the j^(th) grid point acting on the i^(th)pixel, W_(j), is the weight value or the j^(th) interpolating function,and M is the number of points in the grid.
 5. A method of correctingintensity inhomogeneity in an image, said method comprising: generating,using a processor, a histogram from pixel information for an imageportion of an object; and transforming at least one pixel in said pixelinformation by minimizing error between said histogram and a specifiedhistogram, wherein a plurality of grid points overlay said image portionof said object, each said grid point having associated therewith atleast one interpolating function, thereby minimizing said error, andwherein said transforming at least one pixel is not uniformly applied tosaid pixel information for said image portion.
 6. An imaging apparatus,said apparatus comprising: a processor for processing image dataacquired of an image portion of an object, a histogram being generatedtherefrom, wherein said processor transforms pixel information in saidimage data by minimizing error between said histogram of said image dataand a specified histogram, and wherein a plurality of grid pointsoverlay said image portion of said object, each said grid point havingassociated therewith at least one interpolating function, therebyminimizing said error, and wherein said pixel information transformationis not uniformly across said pixel information in said image portion. 7.A method for generating an image of an object, said image comprising: aplurality of pixels therein of an image portion, wherein said pluralityof pixels in said image portion correspond to pixel information of saidobject, said pixel information having image intensity inhomogeneitytherein; and wherein at least one pixel in said pixel information istransformed by minimizing error between a histogram generated from saidpixel information and a specified histogram, thereby correcting saidimage intensity inhomogeneity within said image portion, and forming acorrected image, wherein a plurality of grid points overlay said imageportion of said object, each said grid point having associated therewithat least one interpolating function, thereby minimizing said error, andwherein said pixel information transformation is not uniformly acrosssaid pixel information in said image portion.
 8. An method of correctingintensity inhomogeneity in an imaging machine, said method comprisingthe steps of: scanning an object using said imaging machine; receivingpixel information for an image portion of the object; generating, usinga processor, a histogram; and transforming, using a processor, at leastone pixel in said pixel information by minimizing error between saidhistogram and a specified histogram, wherein a plurality of grid pointsoverlay said image portion of said object, each said grid point havingassociated therewith at least one interpolating function, therebyminimizing said error.
 9. The method according to claim 8, wherein saidstep of transforming comprises: modifying said pixel information;computing said weighting vector by minimizing the error between saidhistogram and said specified histogram; and correcting said pixelinformation using said weighting vector.
 10. The method according toclaim 2, wherein said weighting vector (W) is described by the formula:W=B⁻¹Z.
 11. The method according to claim 10, wherein matrix B andvector Z are described by the formulas: $B = {\begin{bmatrix}{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}^{2}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{M\; i}}} \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2\; i}^{2}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2i}b_{M\; i}}} \\\vdots & \vdots & \; & \vdots \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{1i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}^{2}}}\end{bmatrix}\mspace{20mu}{and}}$ $Z = \begin{bmatrix}{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{1i}}} \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{2i}}} \\\vdots \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{M\; i}}}\end{bmatrix}$ where s_(i) is the histogram specified transformed graylevel of the i^(th) pixel, N is the number of pixels in the image,P_(ij) is the original gray level of the i^(th) pixel, b_(ji) is theinterpolation coefficient of the j^(th) grid point acting on the i^(th)pixel, W_(j), is the weight value of the j^(th) interpolating function,and M is the number of points in the grid.
 12. The method according toclaim 9, wherein said step of computing further comprises: applying tosaid pixel information a plurality of grid points, said grid pointsoverlaying said image of the object, each said grid point havingassociated therewith at least one interpolating function.
 13. The methodaccording to claim 12, wherein said at least one interpolating functionis selected from the group consisting of: Gaussian functions andmultiquadratic basis functions.
 14. The method according to claim 13,wherein said Gaussian function is selected from the group consisting of:two-dimensional Gaussian functions and three-dimensional Gaussianfunctions.
 15. The method according to claim 8, wherein said specifiedhistogram is selected from the group consisting of: uniform histograms,linearly-rising histograms, tissue contrast enhancement histograms,tissue class accentuation histograms and combinations thereof.
 16. Themethod according to claim 8, wherein in said step of receiving pixelinformation for said image of said object, said image of said object isscanned digitally, said image being a digital image having said pixelinformation therein.
 17. The method according to claim 16, wherein saidhistogram is generated from said digital image.
 18. The method accordingto claim 8, wherein said object is an analog image, further comprisingthe step of: converting said analog image into said digital image havingsaid pixel information therein.
 19. The method according to claim 18,wherein said histogram is generated from said digital image.
 20. Imagingapparatus for imaging an object, said apparatus comprising: a processorfor processing the image data acquired, wherein said processortransforms image pixel information by minimizing error between ahistogram of an image portion and a specified histogram, wherein aplurality of grid points overlay said image portion of said object, eachsaid grid point having associated therewith at least one interpolatingfunction, thereby minimizing said error.
 21. The imaging apparatusaccording to claim 20, wherein said processor transforms image pixelinformation by weighting each pixel according to a weighting function.22. The imaging apparatus according to claim 20, wherein said processorin transforming: modifies said pixel information; computes a weightingvector by minimizing the error between said histogram and said specifiedhistogram; and corrects said pixel information using said weightingvector.
 23. The imaging apparatus according to claim 22, wherein saidweighting vector (W) is described by the formula:W=B⁻¹Z.
 24. The imaging apparatus according to claim 23, wherein matrixB and vector Z are described by the formulas: $B = {\begin{bmatrix}{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}^{2}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{M\; i}}} \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2\; i}^{2}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2i}b_{M\; i}}} \\\vdots & \vdots & \; & \vdots \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{1i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}^{2}}}\end{bmatrix}\mspace{20mu}{and}}$ $Z = \begin{bmatrix}{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{1i}}} \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{2i}}} \\\vdots \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{M\; i}}}\end{bmatrix}$ where s_(i) is the histogram specified transformed graylevel of the i^(th) pixel, N is the number of pixels in the image, P_(i)is the original gray level of the i^(th) pixel, b_(ji) is theinterpolation coefficient of the j^(th) grid point acting on the i^(th)pixel, W_(j) is the weight value of the j^(th) interpolating function,and M is the number of points in the grid.
 25. The imaging apparatusaccording to claim 22, wherein said processor in computing: applies tosaid pixel information a plurality of grid points, said grid pointsoverlaying said image data, each said grid point having associatedtherewith at least one interpolating function.
 26. The imaging apparatusaccording to claim 25, wherein said at least one interpolating functionis selected from the group consisting of: Gaussian functions andmultiquadratic basis functions.
 27. The imaging apparatus according toclaim 26, wherein said Gaussian function is selected from the groupconsisting of: two-dimensional Gaussian functions and three-dimensionalGaussian functions.
 28. The imaging apparatus according to claim 20,wherein said specified histogram is selected from the group consistingof: uniform histograms, linearly-rising histograms, tissue contrastenhancement histograms, tissue accentuation histograms and combinationsthereof.
 29. The imaging apparatus of claim 20, wherein said image datais a digital image of said object having said pixel information therein.30. The imaging apparatus of claim 29, wherein said histogram isgenerated from said digital image.
 31. The imaging apparatus of claim29, wherein said image receiver receives said image data in analog,forming an analog image, further comprising: conversion means forconverting said analog image into said digital image having said pixelinformation therein.
 32. A method for generating an image productprepared from a process on an imaging machine, said image comprising:generating, by a processor in said imaging machine, a plurality ofpixels in an image, wherein said plurality of pixels in said imagecorrespond to pixel information of an object imaged by said imagingmachine, said pixel information having image intensity inhomogeneitytherein; and transforming, by a processor in said imaging machine, atleast one pixel in said pixel information by minimizing error between ahistogram generated from said pixel information and a specifiedhistogram, thereby correcting said imaging intensity inhomogeneitywithin said image, and forming a corrected image, wherein a plurality ofgrid points overlay said plurality of pixels of said image, each saidgrid point having associated therewith at least one interpolatingfunction, thereby minimizing said error.
 33. The image according toclaim 32, wherein said at least one pixel is transformed by weightingsaid at least one pixel according to a weighing function.
 34. Theimaging apparatus according to claim 32, wherein said weighting vector(W) is described by the formula:W=B⁻¹Z.
 35. The imaging apparatus according to claim 27, wherein matrixB and vector Z are described by the formulas: $B = {\begin{bmatrix}{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}^{2}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{M\; i}}} \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{1i}b_{2i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2\; i}^{2}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{2i}b_{M\; i}}} \\\vdots & \vdots & \; & \vdots \\{\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{1i}}} & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}b_{2i}}} & \ldots & {\sum\limits_{i = 1}^{N}{P_{i}^{2}b_{M\; i}^{2}}}\end{bmatrix}\mspace{20mu}{and}}$ $Z = \begin{bmatrix}{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{1i}}} \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{2i}}} \\\vdots \\{\sum\limits_{i = 1}^{N}{s_{i}P_{i}b_{M\; i}}}\end{bmatrix}$ where s_(i) is the histogram specified transformed greylevel of the i^(th) pixel, N is the number of pixels in the image, P_(i)is the original gray level of the i^(th) pixel, b_(ji) is theinterpolation coefficient of the j^(th) grid point acting on the i^(th)pixel, W_(j) is the weight value of the j^(th) interpolating function,and M is the number of points in the grid.